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Black-scholes Formula For Valuing European Options; Depreciation - HP 12C Platinum User Manual

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Black-Scholes Formula for Valuing European Options

P = current asset price.
r% = risk-free rate (continuous, per time unit).
s% = volatility (continuous, per time unit).
T = term of option (same time unit as r% and s%).
X = exercise price of option.
N(z) = probability that a unit normal random variable is less than z.
Call Value = P × N(d
Put Value = Call Value + Q – P
where :
d
= LN(P/Q)/v + v/2, d
1
Q = Xe

Depreciation

L
= asset's useful life expectancy.
SBV
= starting book value.
SAL
= salvage value.
FACT
= declining-balance factor expressed as a percentage.
j
= period number.
DPN
= depreciation expense during period j.
j
RDV
= remaining depreciable value at end of period j
j
= RDV
RBV
= remaining book value = RBV
j
Y
= number of months in partial first year.
1
) – Q × N(d
)
1
2
-= d
2
( – T × r % / 1 0 0 )
, v=s%/100×
– DPN
where RDV
j– 1
j
Appendix E: Formulas Used
– v
1
T
= SBV – SAL
0
– DPN
where RBV
j– 1
j
259
= SBV
0

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